log_3⁡〖[(100x^3 ∛(5-x))/(27(x+7)^4 )]〗 needs expantion

log_3⁡〖[(100x^3 ∛(5-x))/(27(x+7)^4 )]〗 needs expantion

 

 

\(log_3⁡\frac{100x^3 \sqrt[3]{5-x}}{27(x+7)^4 }\\ =log_3⁡ [100x^3 \sqrt[3]{5-x}]\quad-\quad [log_327(x+7)^4] \\ =log_3⁡ [100]+log_3⁡ [x^3 ]+log_3⁡ [\sqrt[3]{5-x}]\quad-\quad [log_327+log_3(x+7)^4] \\ =log_3⁡ [100]+log_3⁡ [x^3 ]+log_3⁡ [\sqrt[3]{5-x}]\quad-\quad log_327-log_3(x+7)^4 \\ =log_3⁡ [100]+3log_3⁡ [x ]+\frac{1}{3}log_3⁡ (5-x)\quad-\quad log_33^3-4log_3(x+7) \\ =log_3⁡ [100]+3log_3⁡ [x ]+\frac{1}{3}log_3⁡ (5-x)\quad-\quad 3-4log_3(x+7) \\ \mbox{I am going to stop here because this is not going anywhere.}\)